Re: Problems and Solutions

Cos(Sin A) is always greater than Sin (Cos A), as rightly pointed out by Mathsy!We shall test this for three values in the first quadrant, in degrees.First, 0.01°.Cos (Sin A) > Sin(CosA).Next, for 45° Again, Cos (Sin A) > Sin(CosA).Finally, for 89.9°Yet again, we get the same result. I shall try to search for a proof, or prove it myself!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Re: Problems and Solutions

Two candles A and B, of equal height but different circumferences, burn for 4 hours and 3 hours respectively. If the two are lit at the same time, after what time would one candle be half the height of the other?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Re: Problems and Solutions

As always, you are corect, Mathsy!I shall show how I did it.Assume both candles are 'h' inches in height.The height of the first candle reduces by h/4 every hour and that of the second reduces by h/3.Lets assume in time 't' hours, the first is twice the height of the second.Therefore,h - t(h/4) = 2 [h - t(h/3)]h - ht/4 = 2h - 2ht/3h = 2ht/3 - ht/4h = 5ht/12Cancelling h on both sides,1 = 5t/12or t = 12/5The unit we had taken was hours,therefore, in 12/5 hours, that is 2 2/5 hours, one will be double the height of the other.Simplified, it is 2 hours and 24 minutes.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.